Properties

Label 288990.fc
Number of curves $1$
Conductor $288990$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("fc1")
 
E.isogeny_class()
 

Elliptic curves in class 288990.fc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
288990.fc1 288990fc1 \([1, -1, 1, -72533, -8010323]\) \(-11993263569/972800\) \(-3423033930700800\) \([]\) \(2882880\) \(1.7270\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 288990.fc1 has rank \(1\).

Complex multiplication

The elliptic curves in class 288990.fc do not have complex multiplication.

Modular form 288990.2.a.fc

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + 5 q^{7} + q^{8} - q^{10} - 4 q^{11} + 5 q^{14} + q^{16} + 3 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display